PVST+ - What happens when root bridge disappears?

So currently our L2 network is in shambles, and is just self elected everywhere which is just awful in how things operate.

I was going to do some work to change the priority settings, so I can have a proper primary/secondary in place that will soon. However, I have questions of what would happen if the primary root drops, how quickly would things fail over? Would the next priority level take over after an election, or would it just immediately fail over as everything knows where it belongs? And in either case, when the primary comes up again does it calmly fail over?

My labbing hasn't been very conclusive to help me find an answer I like yet.